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OPEN
Graphene Plasmonic Metasurfaces
to Steer Infrared Light
Zubin Li1,2, Kan Yao3, Fengnian Xia4, Sheng Shen5, Jianguo Tian2 & Yongmin Liu1,3
received: 15 April 2015
accepted: 23 June 2015
Published: 23 July 2015
Metasurfaces utilizing engineered metallic nanostructures have recently emerged as an important
means to manipulate the propagation of light waves in a prescribed manner. However, conventional
metallic metasurfaces mainly efficiently work in the visible and near-infrared regime, and lack
sufficient tunability. In this work, combining the pronounced plasmonic resonance of patterned
graphene structures with a subwavelength-thick optical cavity, we propose and demonstrate novel
graphene metasurfaces that manifest the potential to dynamically control the phase and amplitude
of infrared light with very high efficiency. It is shown that the phase of the infrared light reflected
from a simple graphene ribbon metasurface can span over almost the entire 2π range by changing
the width of the graphene ribbons, while the amplitude of the reflection can be maintained at high
values without significant variations. We successfully realize anomalous reflection, reflective focusing
lenses, and non-diffracting Airy beams based on graphene metasurfaces. Our results open up a new
paradigm of highly integrated photonic platforms for dynamic beam shaping and adaptive optics in
the crucial infrared wavelength range.
Metamaterials are rationally engineered composite materials with exotic properties not easily obtained
or altogether unavailable in nature1–4. Metamaterials have attracted extensive attention from physicists,
material scientists and engineers over the past decade, because they provide unprecedented opportunities
to control light-matter interactions and light propagation in unusual ways. Recently, metasurfaces, a new
class of two-dimensional (2D) metamaterials, have emerged at the frontier of metamaterials research5–7.
In essence, metasurfaces introduce desired phase, amplitude, or polarizatin profiles by patterning planar
subwavelength structures, offering additional, yet important degrees of freedom to mold the flow of light.
Novel optical phenomena and devices based on metasurfaces include anomalous refraction or reflection8,9, strong spin-orbit interaction10,11, ultra-thin focusing or diverging lenses12–14, and holography15,16.
Metasurfaces have also been applied to manipulate near-field surface waves17–20. Compared with their
bulk metamaterial counterparts, the quasi-2D metasurfaces exhibit advantages of increased operation
bandwidth and reduced losses5,6. These new designs are also compatible with planar, low-cost manufacturing and extremely suitable for device integration.
So far, most metasurfaces rely on judiciously designed metallic nanostructures. At optical frequencies,
metallic nanostructures with varied geometries support strong surface plasmon resonances, acting as
local antennas in frequency selective surfaces (FSS)21 that can eventually determine the direction, amplitude and polarization of refracted or reflected beams. However, it is known that the plasmonic response
of metals becomes less pronounced as approaching mid-infrared or longer wavelengths because of the
weaker interaction between electromagnetic waves and electrons22–24. This limits the use of noble metals
in many infrared applications. Graphene, a monolayer of carbon atoms arranged in a honeycomb lattice25,26, has emerged as a promising, alternative candidate for plasmonics at terahertz and mid-infrared
1
Department of Mechanical and Industrial Engineering, Northeastern University, Boston, Massachusetts 02115,
United States. 2Key Laboratory of Weak-Light Nonlinear Photonics, Ministry of Education, TEDA Applied
Physics Institute & School of Physics, Nankai University, Tianjin 300457, China. 3Department of Electrical and
Computer Engineering, Northeastern University, Boston, Massachusetts 02115, United States. 4Department of
Electrical Engineering, Yale University, New Haven, Connecticut 06511, United States. 5Department of Mechanical
Engineering, Carnegie Mellon University, Pittsburgh, Pennsylvania 15213, United States. Correspondence and
requests for materials should be addressed to Y.L. (email: [email protected])
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Figure 1. (a) Schematic of graphene plasmonic metasurfaces, which consist of subwavelength patterned
graphene ribbons on a dielectric/metal substrate. By changing the geometry of the graphene ribbons and
the thickness of the dielectric layer, the resultant plasmonic resonance varies and the reflected infrared
light can be controlled in a prescribed manner. The incident light is not shown for clarity. (b) The graphene
plasmonic metasurface forms an asymmetric Fabry-Perot resonator to substantially enhance the interaction
between light and monolayer graphene structures.
frequencies27–34. Graphene’s electron density, and consequently its plasma frequency, is much lower than
that of bulk noble metals. As a result, graphene is able to support surface plasmons as a bulk metal
does, whereas operating at mid-infrared and lower frequencies. Because of the 2D nature of the platform, graphene surface plasmons exhibit extremely small wavelengths (~λ /10–λ /100) and tight field
confinement on the graphene sheet33,34, while maintaining reasonably small losses in the terahertz and
mid-infrared regime. Indeed, they closely resemble plasmons in the two-dimensional electron gases
(2DEGs) that have been explored before35–37. The strong optical response arising from graphene surface
plasmons also allows us to build novel metamaterials38–40. Moreover, the mechanical, electronic, optical,
and even thermal properties of graphene are highly tunable via chemical doping or electrical gating41–47,
which is impossible or inefficient if metals are used. These favorable features arouse enormous interest
in the investigation of graphene-based tunable plasmonics and metamaterials31,32,38–40,48,49.
Although fairly extensive effort has been devoted to graphene-based metamaterials and plasmonics,
previous work mainly focuses on the distinct resonance features and their spectral tuning. In this letter,
we propose and demonstrate graphene plasmonic metasurfaces to steer infrared light with high efficiency, which drastically expand the functionalities and performance of graphene devices towards complete wave shaping. This is made possible by combining the plasmonic resonance of patterned graphene
nanostructures with a subwavelength-thick optical cavity to enhance the intrinsically weak interaction
between light and single-layer graphene. Furthermore, the graphene metasurfaces can be dynamically
tuned by changing the Fermi energy of graphene via simple chemical or electrostatic tuning that is
unachievable in conventional metasurfaces made of metals. As a proof of principle, we numerically study
graphene metasurfaces consisting of rationally designed graphene ribbons. It is shown that the phase of
the reflected infrared light can range almost from –π to π by tailoring the dimensions of the graphene
ribbons as well as the optical cavity, while the amplitude of the reflectivity is sufficiently high without
substantial variations. This allows us to design graphene metasurfaces to implement anomalous reflection, focusing and non-diffracting Airy beam generation. We envision that such transformative graphene
metasurfaces would open up a new paradigm of integrated photonic systems with multifunctional applications, including dynamic beam shaping, hyperspectral imaging, adaptive optics, biomedical sensing,
and energy harvesting in the critical infrared region.
Results
Graphene can interact with light strongly via plasmonic resonance27,38,39,50,51. However, due to its innate
thinness, light-graphene interactions need to be further enhanced to achieve adequate efficiency for
practical device applications. Towards this goal, we utilize a subwavelength-thick optical cavity, which is
composed of patterned graphene nanostructures, a dielectric spacing layer and an optically thick metal
film as shown in Fig. 1a. This structure can be modeled as an asymmetric Fabry-Perot resonator, that is,
a metasurface reflector as a partially reflecting mirror in the front and a metallic fully reflecting mirror
in the back. When a plane wave is incident on the metasurface, the reflected fields from each interface
interfere with each other (Fig. 1b). Depending on the geometry of the graphene nanostructures, and the
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Figure 2. (a) Reflectivity and (b) relative phase of the reflected light as the functions of ribbon width (w)
and dielectric layer thickness (s). (c) Reflectivity and phase of the reflected light with varied ribbon widths,
while the thickness of the dielectric layer is fixed at s = 4.37 μ m. The inset shows the field distribution at the
cross-section of a graphene ribbon at the plasmonic resonance condition when w = 1.035 μ m. The frequency
of infrared light is 12.32 THz, the refractive index of the dielectric layer is 1.4, and the Fermi energy of
graphene is 0.64 eV in all simulations.
dielectric constant and thickness of the dielectric layer, critical coupling condition can be satisfied even
when the thickness s of the dielectric spacing layer is smaller than the wavelength. Consequently, we can
achieve strong and even perfect absorption with monolayer graphene structures as theoretically proposed
and recently demonstrated in experiments52–55.
Graphene metasurfaces coupled with an optical cavity exhibit much more striking properties and
applications beyond strong absorption. Our numerical simulations show that the phase of the reflected
light can vary from almost –π to π by selecting the width of the graphene ribbons as well as the thickness
of the dielectric spacing layer, while the amplitude of reflectivity remains high and only shows moderate
variations. These two properties allow us to design a variety of planar graphene photonic devices in the
reflective configuration that are easy to fabricate and integrate. It should be emphasized that the full 2π phase coverage is crucial for designing functional metasurfaces, which necessitates the bottom metallic
mirror. The bare graphene ribbons on a dielectric layer only provide a phase modulation range of about
π (Supplementary Information)56, because of its intrinsic Lorenz-like resonance. To cover the full phase
space, one can utilize V-shape antennas or geometric phase by rotating the structures. However, these
two approaches only work for cross-polarization, and the efficiency is generally low8,9,13,57.
In this paper, we focus on the far-infrared region, while the operation wavelength of the proposed
graphene metasurfaces can be readily extended to mid-infrared by scaling the dimension of the graphene
patterns. Figure 2a,b show the reflectivity and the phase of the reflected light with transverse magnetic
(TM) polarization, respectively, as the function of the thickness (s) of the dielectric spacing layer and the
width (w) of the graphene ribbons. TM polarized light can excite the plasmonic resonance of graphene
ribbons. In contrast, for transverse electric (TE) polarization, the electric field is parallel to the graphene
ribbons, and no plasmonic resonance can be excited to modulate the phase and amplitude of reflected
light (Supplementary Information). The frequency of the infrared light is 12.32 THz, which is the resonant frequency for a graphene ribbon with width 1.035 μ m. The periodicity (p) of the graphene ribbon
is fixed at 3 μ m. In the finite element simulation utilizing commercial software COMSOL Multiphysics,
the optical conductivity of graphene is described by Kubo model with the Fermi energy Ef = 0.64 eV.
The refractive index of the dielectric spacing layer is taken as 1.4, and Drude model is applied to fit the
experimental data of permittivity of gold for the back reflective mirror58. More details about the simulation can be found in the Methods session.
From Fig. 2a,b, one can clearly see that there is a pronounced resonance feature when the width of the
graphene ribbons is about 1 μ m. The reflection amplitude and phase vary drastically around this value.
Meanwhile, if we change the substrate thickness, the reflection and the phase show periodic oscillations.
At certain thicknesses, the reflection can drop to almost zero when the width of the graphene ribbons is
within the resonance region. This means that the absorption approaches unity, since the gold back mirror
is optically thick and there is no transmission. Such perfect absorption is consistent with previous published work52,53. At other thicknesses, for example, s = 4.37 μ m, the reflectivity is larger than 48.6% and
the phase smoothly spans over from almost –π to π with different graphene ribbon widths as shown in
Fig. 2c. The finite loss of graphene limits the phase shift range, which is known for a damped oscillator.
In the ideal, lossless case, the phase shift can completely cover the 2π range. The inset of Fig. 2c plots
the amplitude of the electric field within one unit cell of the graphene metasurface at the plasmonic
resonance frequency. It can be seen that the field is extremely confined in the vicinity of the graphene
ribbon, implying negligible interactions between adjacent unit cells. Therefore, the phase diagram calculated from periodic graphene ribbons well represents the intrinsic resonance of individual ribbons rather
than their collective behavior.
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Figure 3. Demonstration of anomalous reflection for (a) normal incidence, and (b) oblique incidence with
the incident angle of 15.0°. In the figures, the incident field has been subtracted, and the plotted Hy field
component of the reflected light is normalized to the incidence. The frequency of infrared light is 12.32 THz
and the Fermi energy of graphene is taken as 0.64 eV. The refractive index of the dielectric spacing layer is
1.4, and its thickness is 4.37 μ m. Graphene ribbons are located at the plane of z = 0.
The results in Fig. 2c indicate that we can achieve high reflectivity larger than 48.6% and a continuous
2π phase modulation by changing the width of the graphene ribbons, enabling design of novel planar
optical devices to steer reflected infrared light with high efficiency. We start with the demonstration of
anomalous reflection. In metasurfaces, new degrees of freedom to control light propagation are attained
by introducing in-plane phase gradient dϕ/dx at the interface between two media. Anomalous reflection and refraction phenomena have been reported in this regime, which are in sharp contrast to the
well-known refraction and reflection law8,9. For the latter case, the relationship between the reflection
angle and incident angle is generalized to
sin (θr ) − sin (θ i) =
λ dϕ
2π ⋅ n i dx
(1)
where ni is the refractive index of the material at the incidence side, and θi and θr are the incident and
reflected angle, respectively. There is a nonlinear relation between θi and θr, distinctly different from
conventional specular reflection. For normal incidence and ni = 1 (air), the reflection angle can be calculated as
 λ dϕ 

θr = sin−1 
 2π dx 
(2)
In our simulation, we set 36 graphene ribbons with periodicity of 3 μ m. The width of each ribbon
is properly selected (Supplementary Information) so that there is 10° phase shift between two adjacent
unit cells. For normally incident light at 12.32 THz, we can deduce that the reflection angle is 13.0° from
the phase front. The full-wave simulation result is shown in Fig. 3a, which plots the magnetic field (Hy)
of the reflected light. According to the field distribution, we can retrieve the reflection angle, which is
about 13.1° and in excellent agreement with the predicted value. The slight deformation of the phase front
arises from the finite periodicity and non-uniform reflectivity of the metasurface. If we set the incident
angle as 15.0°, the reflected angle should be about 29.0°. The simulation result is shown in Fig. 3b, and
we can see that the reflected light is again like a plane wave with its phase front tilted about 28.9° relative
to the surface normal. The overall reflectivity is about 73.9% for normal incidence and 76.0% for 15.0°
incidence, clearly demonstrating the high efficiency of the graphene metasurface.
The second graphene metasurface device to be demonstrated is a reflective focusing lens. To design
such a lens, we must ensure that the light reflected from every graphene ribbon has the same phase
or with 2π multiplied by an arbitrary integer when propagating to the focal point. In other words, the
metasurface should carry a phase profile to compensate the propagation phase between graphene ribbons
and the focal point, so that the radiated waves from the metasurface can constructively interfere with
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Figure 4. Demonstration of reflective focusing lens at three different frequencies: (a) 12.32 THz, (b)
11.82 THz, and (c) 12.82 THz. In the figures, the incident light has been subtracted, and the amplitude of
the reflected light is normalized to the incidence. Material parameters are the same as in Fig. 3. Graphene
ribbons are located at the plane of z = 0.
Figure 5. Dynamically tunable reflective focusing lens by varying the Fermi energy of graphene.
(a) Ef = 0.56 eV and (b) Ef = 0.48 eV. In the figures, the incident light has been subtracted, and the amplitude
of the reflected light is normalized to the incidence. The operation frequency is 12.32 THz. Graphene
ribbons are located at the plane of z = 0.
each other at the focal point. For a certain focal length F, the phase shift distribution ϕ(x) along the
interface should satisfy
ϕ (x ) =
2π
λ
(
F2 + x2 − F
)
(3)
In our study, we set F = 100 μ m, and x = mp with p equal to the periodicity of the graphene ribbons
and m = 0, ± 1, ± 2… From the results presented in Fig. 2c, we can determine the width of graphene ribbons along the x axis (Supplementary Information) to match the phase profile calculated by Equation 3.
The simulation result is shown in Fig. 4a. TM polarized light at frequency f = 12.32 THz is launched
from the top, and perpendicularly impinges upon the graphene metasurface. One can see clearly that
the reflection is efficiently focused. The focal point is at 98.8 μ m, agreeing very well with the original
design at 100 μ m. The small discrepancy between the design and simulation is mainly attributed to the
finite size of the unit cells with respect to the wavelength. In addition, the focusing effect of the graphene
metasurface shows reasonable operation bandwidth. Figures 4b,c present the simulation results at 11.82
and 12.82 THz, respectively. The focusing effect is still preserved, although the field intensity at the focal
point slightly decreases and the focal point shifts about ± 10 μ m compared to Fig. 4a.
The optical property of graphene strongly depends on its carrier concentration, and hence the
Fermi energy of the graphene sheet. This allows us to realize dynamically tunable metasurfaces, which
are impossible or inefficient if metallic nanostructures are employed. In Fig. 5, we compare the same
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Figure 6. Generation of non-diffracting Airy beam. (a) Ideal phase and amplitude at the emitting interface
to generate an Airy beam. (b) Electric filed amplitude of an ideal airy beam. (c) Simplified Airy function.
(d) An Airy beam generated by a graphene metasurface following the simplified design.
graphene focusing metasurface at the same operation frequency of 12.32 THz while reducing the Fermi
energy of graphene from 0.64 eV used in Fig. 4a to 0.56 eV and 0.48 eV, respectively. It can be seen that
the focal point shifts slightly to a longer distance, and the intensity at the focal point significantly reduces.
The focusing effect can be completely turned off when the Fermi energy is about 0.4 eV or smaller. If
we increase the Fermi energy to a value larger than 0.64 eV, similar strong modulation effect is observed
while the focal point slightly moves towards the metasurface. These results manifest a new avenue for
dynamic beam shaping and adaptive optics on a truly 2D platform through simple electrostatic gating.
Finally we employ graphene metasurfaces to generate Airy beams. Airy beams represent the only
possible non-diffracting wave packets in one-dimensional (1D) planar systems59,60. In addition to their
non-diffracting and self-healing properties61, the propagation of Airy beams exhibits a unique self-bending
behavior in the absence of any external potential, which has been exploited for interesting applications
in optical micromanipulation62. Airy beams can be generated by a designed phase and amplitude profile
at the emitting plane, which is given by Airy function (Fig. 6a). The field plot of the resulting ideal Airy
beam is presented in Fig. 6b, showing clearly the exceptional self-bending and non-diffractive feature.
However, the ideal phase and amplitude profile cannot be easily satisfied with graphene ribbons, because
it is very difficult to modulate the phase and the amplitude separately by just changing the width and
periodicity of the ribbons. Fortunately, a simplified yet practical approach is to just consider the phase of
the Airy function and keep the emitting field amplitude constant63. The field amplitude modulation is not
so crucial because of Airy beam’s special self-healing property, which can automatically correct the field
profile along the propagation path even in the presence of defects. The peaks and valleys in Fig. 6a can be
approximated as rectangular profiles with equal magnitudes and a π phase difference as shown in Fig. 6c.
In our simulation, we use two ribbon widths, w1 = 858 nm (for peaks) and w2 = 1058 nm (for valleys) to
match the simplified profile (Supplementary Information). From Fig. 6d one can see that under such an
approximation, the reflected field still well resembles the ideal Airy beam shown in Fig. 6b.
Discussion
We have introduced graphene metasurfaces based on simple ribbon geometries to efficiently steer infrared light in the reflective configuration. The graphene ribbons coupled with a subwavelength-thick
optical cavity substantially enhance the light-graphene interaction, allowing us to achieve almost 2π Scientific Reports | 5:12423 | DOI: 10.1038/srep12423
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phase modulation and high reflectivity amplitude. Anomalous reflection, reflective focusing lenses and
non-diffracting beam generation with capability of dynamic tuning have been successfully demonstrated.
Although we have focused on the far-infrared frequency, the design strategy can be readily applied to
mid-infrared region by varying the dimension of graphene ribbons and thus their plasmonic resonance.
Moreover, extending ribbons to other 2D patterns provides additional degrees of freedom in the design,
promising other important advantages for light steering such as 3D focusing, polarization-independent
functionalities, and strong polarization conversion. Leveraging the remarkable plasmonic properties of
graphene at infrared wavelengths, the graphene metasurfaces demonstrated here manifest unprecedented
control over the electromagnetic properties of materials on a completely 2D platform, which enable disruptive light-weight, ultra-compact, and high-speed optical architectures for diverse applications.
Methods
In the terahertz and infrared region, the optical conductivity of graphene is dominated by the intraband
transition. It can be described by a semi-classical Drude model64,
σ (ω ) =

 E f 
i
 
k B T ⋅ ln 2 cosh 



π
 2k B T   ω + iτ −1

2e 2
2
where kB is the Boltzmann constant, Τ is the temperature, Ef is the absolute value of the Fermi energy,
and τ is the electron relaxation time. When the Fermi energy Ef is much larger than the thermal energy
e2E
kBT, the conductivity of graphene can be further simplified to σ (ω) = 2f i −1 . The electron relaxaπ  ω + iτ
tion time τ is related to the carrier mobility μ, the Fermi energy Ef and Fermi velocity vf as τ = μEf/evf2,
which indicates that increasing carrier mobility of graphene will reduce the loss and improve the device
efficiency. The carrier mobility μ of graphene film ranges from ∼1000 cm2/Vs in chemical vapor deposition (CVD)-grown graphene to 230,000 cm2/Vs in suspended exfoliated graphene. In our simulations,
we assume the Fermi energy of graphene Ef around 0.64 eV, a moderate mobility μ = 10,000 cm2/Vs,
Fermi velocity vf = 106 m/s and scattering time τ = 6.4 × 10−13 s27,30. Please note that the Fermi energy as
high as Ef = 1–2 eV has been reported65,66, and graphene mobility at the level of 10,000 cm2/Vs has been
achieved by using a hexagonal boron nitride substrate even with thickness as small as 14 nm67,68. The
surface conductivity can be converted into a volume conductivity σv = σ/t assuming that t is a very small
value31. Such an approach has been widely used in previous numerical work. However, it imposes significant meshing load and simulation time. In the finite element simulations based on commercial electromagnetic solver COMSOL Multiphysics, we apply transition boundary condition that assigns the
conductivity to a single interface instead of a film with finite thickness. Our comparison results confirm
that this method is consistent with previous one when the thickness of graphene film approaches to
zeros. As a result, we are able to greatly relieve the meshing difficulty, save memory, and shorten the
simulation time. An infrared transparent material, such as Potassium Bromide (KBr), Barium Fluoride
(BaF2), Calcium Fluoride (CaF2), or Magnesium Fluoride (MgF2), is employed in the design as the dielectric spacing layer, which is assumed to have a refractive index of 1.4.
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Acknowledgements
Y. L. acknowledges the financial support of TIER 1 award from Northeastern University. Z. L. acknowledges
the Chinese National Key Basic Research Special Fund (2011CB922003).
Author Contributions
Z.L. and Y.L. conceived the idea. Z.L. and K.Y. performed the simulations. Y.L. and Z.L. wrote the
manuscript. K.Y., F.X., S.S. and J.T. discussed the results, reviewed the manuscript and contributed to
the scientific interpretation.
Scientific Reports | 5:12423 | DOI: 10.1038/srep12423
8
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Additional Information
Supplementary information accompanies this paper at http://www.nature.com/srep
Competing financial interests: The authors declare no competing financial interests.
How to cite this article: Li, Z. et al. Graphene Plasmonic Metasurfaces to Steer Infrared Light. Sci.
Rep. 5, 12423; doi: 10.1038/srep12423 (2015).
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